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Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account…

Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to this are distributional limit laws and we derive a central…

Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…

Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…

In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…

We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the…

Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear programming, our method is based on a dynamical formulation…

Real-world image super-resolution (SR) tasks often do not have paired datasets, which limits the application of supervised techniques. As a result, the tasks are usually approached by unpaired techniques based on Generative Adversarial…

Optimal transport (OT) theory provides powerful tools to compare probability measures. However, OT is limited to nonnegative measures having the same mass, and suffers serious drawbacks about its computation and statistics. This leads to…

The relevance of optimal transport methods to machine learning has long been hindered by two salient limitations. First, the $O(n^3)$ computational cost of standard sample-based solvers (when used on batches of $n$ samples) is prohibitive.…

Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…

We propose a new regularized optimal transport (OT) formulation, termed sliced-regularized optimal transport (SROT). Unlike entropic OT (EOT), which regularizes the transport plan toward an independent coupling, SROT regularizes it toward a…

Mini-batch optimal transport (m-OT) has been successfully used in practical applications that involve probability measures with a very high number of supports. The m-OT solves several smaller optimal transport problems and then returns the…

Optimal transport maps and plans between two absolutely continuous measures $\mu$ and $\nu$ can be approximated by solving semi-discrete or fully-discrete optimal transport problems. These two problems ensue from approximating $\mu$ or both…

We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…

We introduce a general framework for testing statistical hypotheses for probability measures supported on finite spaces, which is based on optimal transport (OT). These tests are inspired by the analysis of variance (ANOVA) and its…

The interaction data used by recommender systems (RSs) inevitably include noises resulting from mistaken or exploratory clicks, especially under implicit feedbacks. Without proper denoising, RS models cannot effectively capture users'…